"[ISIS] is expanding. It's not contained. It's in more than a dozen countries now," Feinstein said.

Feinstein said she doesn't believe administration officials' claim that while ISIS has an ambition to target the U.S., they don't have the capability.

"Now they're doing major attacks. One in Beirut, 40 people killed. The Russian airliner over Sinai, 224 people killed. The events in Paris, this last weekend...129 people killed, with over 100 wounded," she said. "I think they do have the capability to hit in the United States."

Sen. John McCain, R-Arizona, chairman of the Senate Armed Services Committee, told CBS News' Nancy Cordes that the debacle over the plan to accept additional Syrian refugees is a result of the president's "failed" leadership.

"This is the symptom of the problem that was created by the president's failed non-existent strategy and therefore, these are the consequences of a failed strategy, which has led to the chaos, the quarter of a million of people who are dead, the millions of refugees. This president hasn't led," McCain said.

"There will be an intensification of the strategy that we've put forward but the strategy that we are putting forward is the strategy that ultimately is going to work," the president said. "It's going to take time."

"The President is wrong. ISIS is not contained," Rep. Ted Poe, R-Texas, said on the House floor Monday following the president's remarks. "Shall we dither until this Capital is bombed? I think not."

Rep. Tulsi Gabbard, D-Hawaii, who served in the Iraq war, said on CNN that the Obama administration must stop "this illegal counterproductive war" to overthrow Syrian President Bashar al-Assad.

"It's counterproductive because it is working towards the exact same objective that ISIS, al Qaeda and these other Islamic extremist groups are trying to achieve," she said. "If they achieve that, they will have all of that territory under their command."

Instead, Gabbard recommends that the U.S. should directly supply heavy weapons to the Kurds and Peshmerga. Asked if she thinks U.S. troops should be deployed to the region to fight on the ground, she said, "Absolutely not. I think it would be counterproductive to our goal, our mission."

Senate Majority Leader Mitch McConnell, R-Kentucky, said on the Senate floor Monday night that he hopes the president works cooperatively with both parties going forward.

At the House GOP leadership press conference Tuesday, Rep. Martha McSally, R-Arizona, who served in the Air Force, slammed the president.

"This administration needs to step up. We do not have a strategy. We do not have a focus," she said.